Duality and infinite dimensional optimization

The purpose is to, establish various duality theorems, including a generalization of the Fenchel duality theorem of Attouch and Brezis to convex processes under relaxed interiority conditions and show the usefulness of the Attouch and Brezis type conditions in optimization. The significance of the interiority conditions is that they provide easily verifiable conditions for a large class of infinite dimensional convex programs; whereas the standard Slater constraint qualification fails. The results are applied to obtain duality theorems for general systems of inequalities and minimax results

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